From bd6db9979a0820243ba4d522a3182b09f6454fc6 Mon Sep 17 00:00:00 2001 From: Andrew Jackson Date: Wed, 10 Jun 2020 16:35:37 +0100 Subject: [PATCH] minor edit to source-aggregation --- aj-content/practicals/source-aggregation.Rmd | 2 +- .../practicals/source-aggregation.nb.html | 350 +++++++++++++++--- 2 files changed, 309 insertions(+), 43 deletions(-) diff --git a/aj-content/practicals/source-aggregation.Rmd b/aj-content/practicals/source-aggregation.Rmd index 0586a37..bb166e6 100644 --- a/aj-content/practicals/source-aggregation.Rmd +++ b/aj-content/practicals/source-aggregation.Rmd @@ -163,7 +163,7 @@ Far more honest is to fit the model as before, with the sources as we believe th ```{r a-posteriori} # combine sources C and D which are in positions 3 and 4 -simmr_out_a_posteriori <- simmr::combine_sources( +simmr_out_a_posteriori <- combine_sources( simmr_out, to_combine = simmr_out$input$source_names[c(3,4)], new_source_name = "CD") diff --git a/aj-content/practicals/source-aggregation.nb.html b/aj-content/practicals/source-aggregation.nb.html index b8c6313..870201a 100644 --- a/aj-content/practicals/source-aggregation.nb.html +++ b/aj-content/practicals/source-aggregation.nb.html @@ -1805,6 +1805,9 @@

Create some simulated data for us to work with

plot(simmr_in) + +

+ @@ -1813,27 +1816,186 @@

Fit the SIMM

We can fit a simmr model using the defaults, and here supress the output using the results='hide' option in the chunk.

+ +
simmr_out = simmr_mcmc(simmr_in)
+

And we should always check for convergence.

- + 
# a summary table of convergence diagnostics
-summary(simmr_out,type='diagnostics')
-
-# plot the posterior predictive power 
+summary(simmr_out,type='diagnostics')
+ + +

+Summary for 1 
+Gelman diagnostics - these values should all be close to 1.
+If not, try a longer run of simmr_mcmc.
+deviance        A        B        C        D   sd[dC]   sd[dN] 
+       1        1        1        1        1        1        1
+ + +
# plot the posterior predictive power 
 posterior_predictive(simmr_out)
+ +
Compiling model graph
+   Resolving undeclared variables
+   Allocating nodes
+Graph information:
+   Observed stochastic nodes: 20
+   Unobserved stochastic nodes: 26
+   Total graph size: 141
+
+Initializing model
+
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+ + +

+

The results of this toy example are not expected to be overly helpful or meaningful.

- -
summary(simmr_out,type='statistics')
-summary(simmr_out,type='quantiles')
+ +
summary(simmr_out,type='statistics')
+ + +

+Summary for 1 
+           mean    sd
+deviance 15.542 3.644
+A         0.245 0.069
+B         0.254 0.069
+C         0.249 0.069
+D         0.252 0.069
+sd[dC]    0.163 0.137
+sd[dN]    0.162 0.135
+ + +
summary(simmr_out,type='quantiles')
+ +

+Summary for 1 
+           2.5%    25%    50%    75%  97.5%
+deviance 10.683 12.878 14.848 17.393 24.827
+A         0.103  0.201  0.245  0.291  0.379
+B         0.121  0.206  0.254  0.299  0.394
+C         0.108  0.205  0.248  0.296  0.384
+D         0.119  0.206  0.252  0.297  0.395
+sd[dC]    0.006  0.061  0.130  0.230  0.507
+sd[dN]    0.006  0.058  0.130  0.230  0.484
+

Plot the estimates of the dietary proportions

@@ -1843,6 +2005,9 @@

Fit the SIMM

# Plot the a priori aggregated diet estimatess
 plot(simmr_out, type = "density")
+ +

+

Plot the covariance between the estimated dietary proportons in the posterior.

@@ -1853,6 +2018,9 @@

Fit the SIMM

plot(simmr_out, type = "matrix") + +

+ @@ -1861,26 +2029,6 @@

A priori aggregation

We combine the sources C and D before we run the model as is sometimes suggested. We do this by taking the mean of the means, and we square the SDs to make them variances, then add them, and then square-root them to turn them back into SDs again. We dont need to change the consumer data in any way.

- -

-# specify the source names
-S_names_a_priori = c("A","B","CD")
-
-# take the mean of the last two sources C and D
-S_means_a_priori = rbind(S_means[1:2,], colMeans(S_means[3:4,]) )
-
-# square the sds for sources C and D to convert to variance,
-# sum them and convert back to sd
-S_sds_a_priori = rbind( S_sds[1:2,], colSums(S_sds[3:4,]^2) ^ 0.5 )
-
-# and create the new simmr object
-# here we have no TDFs or concentration values
-simmr_in_a_priori <- simmr_load(mixtures = consumers,
-                       source_names = S_names_a_priori,
-                       source_means = S_means_a_priori,
-                       source_sds = S_sds_a_priori)
-
-

Plot this newly combined data.

@@ -1890,16 +2038,136 @@

A priori aggregation

# plot the raw data for the a priori aggregated example
 plot(simmr_in_a_priori)
+ +

+

Run the model on the a priori combined data.

- + 
# fit the a priori aggregated models
-simmr_out_a_priori = simmr_mcmc(simmr_in_a_priori)
-
+simmr_out_a_priori = simmr_mcmc(simmr_in_a_priori) + +
Compiling model graph
+   Resolving undeclared variables
+   Allocating nodes
+Graph information:
+   Observed stochastic nodes: 20
+   Unobserved stochastic nodes: 5
+   Total graph size: 107
+
+Initializing model
+
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+

And plot

@@ -1909,6 +2177,9 @@

A priori aggregation

# Plot the a priori aggregated diet estimatess
 plot(simmr_out_a_priori, type = "density")
+ +

+

… and now apparently we are very sure about the contributions of all sources to the diet. There is some correlation between A and B since they need to balance each other out in combination to yield a dB value of 0. You would now incorrectly assume that CD represents pretty much a guaranteed 43% of the diet.

@@ -1919,6 +2190,9 @@

A priori aggregation

plot(simmr_out_a_priori, type = "matrix") + +

+ @@ -1927,17 +2201,9 @@

A posteriori aggregation

Far more honest is to fit the model as before, with the sources as we believe them to be a priori and then simply add our prortions together from the posterior distribution. This is made very easy in SIMMR and also MixSIAR with dedicated functions. In fact, MixSIAR also allows easier a priori aggregation by hiding the routine outlined in the preceding section.

- -
# combine sources C and D which are in positions 3 and 4
-simmr_out_a_posteriori <- simmr::combine_sources(
-  simmr_out, 
-  to_combine = simmr_out$input$source_names[c(3,4)], 
-  new_source_name = "CD")
-
-# Plot the a posteriori aggregated diet estimatess
-plot(simmr_out_a_posteriori, type = "density")
-
- + +

+

This result fits much better with what we would predict: that if the model is still not sure about the contribution of the four sources to the mixture, but that it is pretty sure that on average, 50% of the diet is comprised of both C and D. This concept continues until the model is entirely certain, with no error, that the diet is wholly 100% of A+B+C+D.

@@ -1945,7 +2211,7 @@

A posteriori aggregation

-
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